Code runtime optimization-the task of rewriting a given code to a faster one-remains challenging, as it requires reasoning about performance trade-offs involving algorithmic and structural choices. Recent approaches employ code-LLMs with slow-fast code pairs provided as optimization guidance, but such pair-based methods obscure the causal factors of performance gains and often lead to superficial pattern imitation rather than genuine performance reasoning. We introduce ECO, a performance-aware prompting framework for code optimization. ECO first distills runtime optimization instructions (ROIs) from reference slow-fast code pairs; Each ROI describes root causes of inefficiency and the rationales that drive performance improvements. For a given input code, ECO in parallel employs (i) a symbolic advisor to produce a bottleneck diagnosis tailored to the code, and (ii) an ROI retriever to return related ROIs. These two outputs are then composed into a performance-aware prompt, providing actionable guidance for code-LLMs. ECO's prompts are model-agnostic, require no fine-tuning, and can be easily prepended to any code-LLM prompt. Our empirical studies highlight that ECO prompting significantly improves code-LLMs' ability to generate efficient code, achieving speedups of up to 7.81x while minimizing correctness loss.